2 papers
math.DG2020
The classification of flat Riemannian metrics on the plane
Vincent E. Coll, Lee B. Whitt
We classify all smooth flat Riemannian metrics on the two-dimensional plane. In the complete case, it is well-known that these metrics are isometric to the Euclidean metric. In the…
math.DG2019
The Flat Plane and a Constructive Proof of Minding's Theorem
Vincent E. Coll, Lee B. Whitt
Minding's most celebrated result is his namesake theorem of 1839 which established that all surfaces having the same constant curvature must be locally isometric. Today, Minding's…